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# Data Gathering

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Two number cubes are rolled to determine how a token moves on a game board. The sides of each number cube are numbered 1, 2, 3, 4, 5 and 6.

There are two options describing how the token will be moved.

Option A: If the product is even, move forward 4 spaces. Otherwise, move backward 8.

Option B: If the product is even, move forward 5 spaces. Otherwise, move backward 9.

Use mathematical expectation to determine which option offers the greater likelihood of moving closer to the finish line on the game board.

Which statement best explains the better option?

A) The mathematical expectation of Option A is 1.5. The mathematical expectation of Option B is 1. Option A offers a greater likelihood of advancing to the finish line.

B) The mathematical expectation of Option A is 1. The mathematical expectation of Option B is 1.5. Option A offers a greater likelihood of advancing to the finish line.

C) The mathematical expectation of Option A is 1. The mathematical expectation of Option B is 1.5. Option B offers a greater likelihood of advancing to the finish line.

D) The mathematical expectation of Option A is 1.5. The mathematical expectation of Option B is 1. Option B offers a greater likelihood of advancing to the finish line.

May 19, 2021

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Product Table

1  2   3   4    5   6

1      1/2 even

2       all  even

3      1/2 even

4      all  even

5      1/2 even

6       all even

36  outcomes .....   3(3) + 3(6)  =  27  are  even      9   are   odd

First  option  expectation = option A

(4)(27/36)  - 8 ( 9/36)   =  3  -  2    =   1

Second  option expectation = option B

(5/)(27/36) - 9( 9/36)   =  15/4  - 9/4  = 6/4  =  3/2  = 1.5

Second option  is  better......."C"  is correct   May 19, 2021